2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62000We give a closed-form formula for the Hilbert function of the tangent cone at the identity of a Schubert variety X in the Grassmannian in both group theoretic and combinatorial terms. We also give a formula for the multiplicity of X at the identity, and a Grobner basis for the ideal defining the intersection of X with the opposite cell as a closed subvariety of the opposite cell. We give conjectures for the Hilbert function and multiplicity at points other than the identity.11 pagesAlgebraic Geometry14M15text